remove Gamma from Bessels.jl and add dep to Gamma.jl

Project.toml

@@ -3,6 +3,7 @@ uuid = "0e736298-9ec6-45e8-9647-e4fc86a2fe38"
 version = "0.3.0-DEV"
 
 [deps]
+Gamma = "a0844989-3bd2-4988-8bea-c9407ab0941b"
 SIMDMath = "5443be0b-e40a-4f70-a07e-dcd652efc383"
 
 [weakdeps]
@@ -13,6 +14,7 @@ BesselsEnzymeCoreExt = "EnzymeCore"
 
 [compat]
 EnzymeCore = "0.7, 0.8"
+Gamma = "1.0.0"
 SIMDMath = "0.2.5"
 julia = "1.9"
 

README.md

@@ -13,7 +13,7 @@ Numerical routines for computing Bessel, Airy, and Hankel functions for real arg
 
 The goal of the library is to provide high quality numerical implementations of Bessel functions with high accuracy without comprimising on computational time. In general, we try to match (and often exceed) the accuracy of other open source routines such as those provided by [SpecialFunctions.jl](https://github.com/JuliaMath/SpecialFunctions.jl). There are instances where we don't quite match that desired accuracy (within a digit or two) but in general will provide implementations that are 5-10x faster (see [benchmarks](https://github.com/JuliaMath/Bessels.jl#benchmarks)).
 
-The library currently supports Bessel functions, modified Bessel functions, Hankel functions, spherical Bessel functions, and Airy functions of the first and second kind for positive real arguments and integer and noninteger orders. Negative arguments are also supported only if the return value is real. [Limited support](https://github.com/JuliaMath/Bessels.jl#complex-numbers) is provided for complex arguments. An unexported gamma function is also provided.
+The library currently supports Bessel functions, modified Bessel functions, Hankel functions, spherical Bessel functions, and Airy functions of the first and second kind for positive real arguments and integer and noninteger orders. Negative arguments are also supported only if the return value is real. [Limited support](https://github.com/JuliaMath/Bessels.jl#complex-numbers) is provided for complex arguments.
 
 # Quick start
 
@@ -184,7 +184,7 @@ Stacktrace:
    @ REPL[62]:1
 ```
 #### Gamma
-We also provide an unexported gamma function for real arguments that can be called with `Bessels.gamma(x)`.
+We also provide an unexported gamma function for real arguments that can be called with `Bessels.gamma(x)`, but this is just a re-export from `Gamma.jl` so if you only want a Gamma function, you should use `Gamma.jl` rather than `Bessels.jl`.
 
 # Accuracy
 

docs/src/API.md

@@ -53,8 +53,3 @@ airyaiprime
 airybi
 airybiprime
 ```
-
-# Gamma functions
-```@docs
-Bessels.gamma
-```

docs/src/index.md

@@ -4,11 +4,11 @@
 
 Bessels.jl is a collection of mathematical algorithms to compute special functions written entirely in the Julia programming language. It is focused on providing high quality implementations of mathematical functions that are accurate and highly performant. Since it contains only Julia code and has no external dependencies, it is a lightweight package that can be used in any high performance application while taking advatnage of the dynamism of the Julia language.
 
-Bessels.jl contains numerous definitions of special functions important in many fields of mathematical physics. Available functions include Bessel, Modified Bessel, Spherical Bessel, Airy, Hankel, and Gamma functions. A full list of available functions can be found in the API section of this documentation. Initial development has focused on providing implementations for real arguments, however, some functions (e.g., Airy) also accept complex numbers as input.
+Bessels.jl contains numerous definitions of special functions important in many fields of mathematical physics. Available functions include Bessel, Modified Bessel, Spherical Bessel, Airy, and Hankel functions. A full list of available functions can be found in the API section of this documentation. Initial development has focused on providing implementations for real arguments, however, some functions (e.g., Airy) also accept complex numbers as input.
 
 ## Scope
 
-Bessels.jl started simply as a package to compute just the Bessel function of the first kind and zero order, but it has quickly grown to include several Bessel type functions. As mentioned earlier, Bessels.jl contains algorithms for computing Bessel, Modified Bessel, Spherical Bessel, Airy, and Hankel functions. These functions are contained in Chapters 9 and 10 of the [NIST Digital Library of Mathematical Functions](https://dlmf.nist.gov/). However, there exists other types of related functions such as the Struve and Weber type functions contained in Chapters 11 and 12. In general, these are special cases of the confuent hypergeometric functions $_0F_1, _1F_1$, and $_1F_2$. Additionally, several other special functions such as the gamma functions are also needed to compute these types of functions.
+Bessels.jl started simply as a package to compute just the Bessel function of the first kind and zero order, but it has quickly grown to include several Bessel type functions. As mentioned earlier, Bessels.jl contains algorithms for computing Bessel, Modified Bessel, Spherical Bessel, Airy, and Hankel functions. These functions are contained in Chapters 9 and 10 of the [NIST Digital Library of Mathematical Functions](https://dlmf.nist.gov/). However, there exists other types of related functions such as the Struve and Weber type functions contained in Chapters 11 and 12. In general, these are special cases of the confuent hypergeometric functions $_0F_1, _1F_1$, and $_1F_2$.
 
 Therefore, Bessels.jl seeks to be home to any Bessel or related functions (see the section provided by [mpmath](https://mpmath.org/doc/current/functions/bessel.html)) which are typically contained in Chapters 9-12 of the NIST Digital library or to any other related function required to compute Bessel type functions.
 
@@ -64,4 +64,4 @@ If you are using Bessels.jl, please feel free to add yours to the list!
 - [Cephes](https://netlib.org/cephes/)
 - [fortran-bessels](https://github.com/perazz/fortran-bessels)
 
-This is by no means exhaustive so please add yours or any others that should be listed.
+This is by no means exhaustive so please add yours or any others that should be listed.

src/BesselFunctions/BesselFunctions.jl

@@ -1,6 +1,6 @@
 module BesselFunctions
 
-using ..GammaFunctions
+using Gamma: gamma, loggamma
 using ..Math
 
 export besselj0
@@ -57,4 +57,4 @@ include("Float128/constants.jl")
 include("Float128/besselj.jl")
 include("Float128/bessely.jl")
 
-end
+end

src/BesselFunctions/besselj.jl

@@ -415,11 +415,11 @@ besselj_series_cutoff(v, x::Float64) = (x < 7.0) || v > (2 + x*(0.109 + 0.062*x)
 # cutoff for Float128 for ~1e-35 relative error
 #besselj_series_cutoff(v, x::AbstractFloat) = (x < 4.0) || v > (x*(0.08 + 0.12*x))
 
+
 #=
 # this needs a better way to sum these as it produces large errors
 # use when v is large and x is small
 # though when v is large we should use the debye expansion instead
-# also do not have a julia implementation of loggamma so will not use for now
 function log_besselj_small_arguments_orders(v, x::T) where T
     MaxIter = 3000
     out = zero(T)

src/BesselFunctions/bessely.jl

@@ -403,7 +403,7 @@ end
 # this also works well for nu > 1.35x - 4.5
 # for nu > 25 more cancellation occurs near integer values
 # There could be premature underflow when (x/2)^v == 0.
-# It might be better to use logarithms (when we get loggamma julia implementation)
+# It might be better to use logarithms, now that we have loggamma julia implementation
 """
     bessely_power_series(nu, x::T) where T <: Float64
 

src/Bessels.jl

@@ -40,12 +40,13 @@ export airybix
 export airybiprime
 export airybiprimex
 
+
+using Gamma
+
 include("Math/Math.jl")
-include("GammaFunctions/GammaFunctions.jl")
 include("AiryFunctions/AiryFunctions.jl")
 include("BesselFunctions/BesselFunctions.jl")
 
-using .GammaFunctions
 using .AiryFunctions
 using .BesselFunctions
 

test/runtests.jl

@@ -7,12 +7,10 @@ import SpecialFunctions
 @time @testset "besselj" begin include("besselj_test.jl") end
 @time @testset "bessely" begin include("bessely_test.jl") end
 @time @testset "hankel" begin include("hankel_test.jl") end
-@time @testset "gamma" begin include("gamma_test.jl") end
 @time @testset "airy" begin include("airy_test.jl") end
 @time @testset "sphericalbessel" begin include("sphericalbessel_test.jl") end
-
 # https://github.com/EnzymeAD/Enzyme.jl/issues/2699
-if VERSION > v"1.12"
+if VERSION > v"1.12-"
     @warn "Skipping enzyme autodiff tests on Julia > 1.12 due to Enzyme.jl compatibility issues."
 else
     @time @testset "besselk enzyme autodiff" begin include("besselk_enzyme_test.jl") end